Among the variety of antenna assemblies (e.g., reflectors) that have been proposed for airborne and spaceborne applications are those unfurlable structures which employ an inflatable structure that forms a 'stressed skin' type of reflective surface. In assemblies proposed to date, non-limiting examples of which are described in U.S. Pat. Nos. 4,364,053 and 4,755,819, the inflatable structure itself often serves as the reflective surface of the antenna. For this purpose, the inflatable material has a preformed reflective shape, so that, once fully inflated, its surface will assume the desired antenna geometry. A significant drawback to such structures is the fact that should there be a change in inflation pressure, most notably a decrease in pressure over time, the contour of the support structure and therefore that of the reflective surface itself, will change from the intended antenna profile, thereby impairing the energy gathering and focussing properties of the antenna.